- Sigma Mühendislik ve Fen Bilimleri Dergisi
- Vol: 37 Issue: 4
- THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF TH...
THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS
Authors : Şuayip Toprakseven
Pages : 1129-1137
View : 7 | Download : 2
Publication Date : 2019-12-01
Article Type : Research
Abstract :In this paper, a Lyapunov-type inequality and the existence of the positive solutions for boundary value problems of the nonlinear fractional Caputo-Fabrizio differential equation have been presented. By using the Guo Krasnoselskii’s fixed point theorem on cone and the properties of the associated Green`s function, we prove the existence of the positive solution. Finally, we gave some numerical examples to validate the theoretical findings.Keywords : Lyapunov-type inequality, fractional Caputo-Fabrizio derivative, Green’s function, positive solution, fixed point.